Compound mold and structured surface articles containing geometric structures with compound faces and method of making same

ABSTRACT

A structured surface articles such as molds or sheeting are formed on a compound substrate including a machined substrate and a replicated substrate. In one embodiment, the structured surface is a cube corner element on a compound substrate. In another embodiment, the structured surface is a geometric structure that has a plurality of faces, where one face is located on the machined substrate and another face is located on the replicated substrate. In yet another embodiment, at least some of the faces include a compound face with a portion formed on the machined substrate and a portion formed on the replicated substrate. The method of making a structured surface article including a geometric structure having a plurality of faces includes forming an array of geometric structures in a first surface of a machined substrate; passivating selected locations of the first surface of the machined substrate; forming a replicated substrate of the machined substrate to form a compound substrate; forming an array of second geometric structures on a second surface opposite the first surface on the machined substrate; and removing selected portions from the second surface of the machined substrate.

BACKGROUND

[0001] The present invention relates generally to structured surfacesfabricated using microreplication techniques. The invention hasparticular application to structured surfaces that compriseretroreflective cube corner elements.

[0002] The reader is directed to the glossary at the end of thespecification for guidance on the meaning of certain terms used herein.

[0003] It is known to use microreplicated structured surfaces in avariety of end use applications such as retroreflective sheeting,mechanical fasteners, and abrasive products. Although the descriptionthat follows focuses on the field of retroreflection, it will beapparent that the disclosed methods and articles can equally well beapplied to other fields that make use of microreplicated structuredsurfaces.

[0004] Cube corner retroreflective sheeting typically comprises a thintransparent layer having a substantially planar front surface and a rearstructured surface comprising a plurality of geometric structures, someor all of which include three reflective faces configured as a cubecorner element.

[0005] Cube corner retroreflective sheeting is commonly produced byfirst manufacturing a master mold that has a structured surface, suchstructured surface corresponding either to the desired cube cornerelement geometry in the finished sheeting or to a negative (inverted)copy thereof, depending upon whether the finished sheeting is to havecube corner pyramids or cube corner cavities (or both). The mold is thenreplicated using any suitable technique such as conventional nickelelectroplating to produce tooling for forming cube cornerretroreflective sheeting by processes such as embossing, extruding, orcast-and-curing. U.S. Pat. No. 5,156,863 (Pricone et al.) provides anillustrative overview of a process for forming tooling used in themanufacture of cube corner retroreflective sheeting. Known methods formanufacturing the master mold include pin-bundling techniques, laminatetechniques, and direct machining techniques. Each of these techniqueshas its own benefits and limitations.

[0006] In pin bundling techniques, a plurality of pins, each having ageometric shape such as a cube corner element on one end, are assembledtogether to form a master mold. U.S. Pat. Nos. 1,591,572 (Stimson) and3,926,402 (Heenan) provide illustrative examples. Pin bundling offersthe ability to manufacture a wide variety of cube corner geometry in asingle mold, because each pin is individually machined. However, suchtechniques are impractical for making small cube corner elements (e.g.those having a cube height less than about 1 millimeter) because of thelarge number of pins and the diminishing size thereof required to beprecisely machined and then arranged in a bundle to form the mold.

[0007] In laminate techniques, a plurality of plate-like structuresknown as laminae, each lamina having geometric shapes formed on one end,are assembled to form a master mold. Laminate techniques are generallyless labor intensive than pin bundling techniques, because the number ofparts to be separately machined is considerably smaller, for a givensize mold and cube corner element. However, design flexibility suffersrelative to that achievable by pin bundling. Illustrative examples oflaminate techniques can be found in U.S. Pat. No. 4,095,773 (Lindner);International Publication No. WO 97/04939 (Mimura et al.); and U.S.application Ser. No. 08/886,074, “Cube Corner Sheeting Mold and Methodof Making the Same”, filed Jul. 2, 1997.

[0008] In direct machining techniques, series of grooved side surfacesare formed in the plane of a planar substrate to form a master mold. Inone well known embodiment, three sets of parallel grooves intersect eachother at 60 degree included angles to form an array of cube cornerelements, each having an equilateral base triangle (see U.S. Pat. No.3,712,706 (Stamm)). In another embodiment, two sets of grooves intersecteach other at an angle greater than 60 degrees and a third set ofgrooves intersects each of the other two sets at an angle less than 60degrees to form an array of canted cube corner element matched pairs(see U.S. Pat. No. 4,588,258 (Hoopman)). Direct machining techniquesoffer the ability to accurately machine very small cube corner elementsin a manner more difficult to achieve using pin bundling or laminatetechniques because of the latter techniques' reliance on constituentparts that can move or shift relative to each other, and that mayseparate from each other, whether during construction of the mold or atother times. Further, direct machining techniques produce large areastructured surfaces that generally have higher uniformity and fidelitythan those made by pin bundling or laminate techniques, since, in directmachining, a large number of individual faces are typically formed in acontinuous motion of the cutting tool, and such individual facesmaintain their alignment throughout the mold fabrication procedure.

[0009] However, a significant drawback to direct machining techniqueshas been reduced design flexibility in the types of cube corner geometrythat can be produced. By way of example, the maximum theoretical totallight return of the cube corner elements depicted in the Stamm patentreferenced above is approximately 67%. Since the issuance of thatpatent, structures and techniques have been disclosed which greatlyexpand the variety of cube corner designs available to the designerusing direct machining. See, for example, U.S. Pat. Nos. 4,775,219(Appledorn et al.); 4,895,428 (Nelson et al.); 5,600,484 (Benson etal.); 5,696,627 (Benson et al.); and 5,734,501 (Smith). Some of the cubecorner designs disclosed in these later references can exhibit effectiveaperture values well above 67% at certain observation and entrancegeometry.

[0010] Nevertheless, an entire class of cube corner elements, referredto herein as “preferred geometry” or “PG” cube corner elements, have upuntil now remained out of reach of known direct machining techniques. Asubstrate incorporating one type of PG cube corner element is shown inthe top plan view of FIG. 1. The cube corner elements shown there eachhave three square faces, and a hexagonal outline in plan view. One ofthe PG cube corner elements is highlighted in bold outline for ease ofidentification. The highlighted cube corner element can be seen to be aPG cube corner element because it has a non-dihedral edge (any one ofthe six edges that have been highlighted in bold) that is inclinedrelative to the plane of the structured surface, and such edge isparallel to adjacent nondihedral edges of neighboring cube cornerelements (each such edge highlighted in bold is not only parallel to butis contiguous with nondihedral edges of its six neighboring cube cornerelements).

[0011] Disclosed herein are methods for making geometric structures,such as PG cube corner elements, that make use of direct machiningtechniques. Also disclosed are molds to manufacture articles accordingto such methods, such articles characterized by having at least onespecially configured compound face.

BRIEF SUMMARY

[0012] Structured surface articles such as molds or sheeting are formedon a compound substrate comprising a machined substrate and a replicatedsubstrate. In one embodiment, the structured surface is a cube cornerelement on a compound substrate. In another embodiment, the structuredsurface comprises a geometric structure that has a plurality of faces,where one face is located on the machined substrate and another face islocated on the replicated substrate. The geometric structure canoptionally be a cube corner element or a PG cube corner element.

[0013] In yet another embodiment, at least some of the faces comprise acompound face with a portion formed on the machined substrate and aportion formed on the substantially replicated substrate. A transitionline may separate the portion of a compound face located on the machinedsubstrate from the portion located on the replicated substrate. Theportion of the compound face on the machined substrate and the portionon the replicated substrate typically have angular orientations thatdiffers by less than 10 degrees of arc.

[0014] Another embodiment is directed to a geometric structure having aplurality of faces disposed on a compound substrate. The compoundsubstrate comprises a machined substrate having a structured surface anda substantially replicated substrate bonded along only a portion of aninterface with the machined substrate.

[0015] In another embodiment, the compound substrate comprises asubstantially replicated substrate having a structured surface and adiscontinuous machined substrate covering only a portion of thestructured surface. The compound substrate also comprises at least onegeometric structure having at least one face disposed on the structuredsurface and at least another face disposed on the machined substrate.

[0016] Another embodiment is directed to a compound substrate comprisinga substantially replicated substrate and a machined substrate. Thereplicated substrate has a structured surface and the machined substratedisposed in discrete pieces on the structured surface.

[0017] Another embodiment is directed to a compound mold having astructured surface comprising cavities formed in a replicated substrateand a plurality of pyramids bordering the cavities that are machined atleast in part in a machined substrate of the compound substrate.

[0018] Cube corner elements, and structured surfaces incorporating anarray of such elements, are disclosed wherein at least one face of thecube corner element terminates at a nondihedral edge of such element,the face comprising two constituent faces disposed on opposed sides of atransition line that is nonparallel to the nondihedral edge. The cubecorner element can comprise a PG cube corner element where some or allof such elements comprise two constituent faces disposed on opposedsides of a transition line that is nonparallel to the respectivenondihedral edge and the transition line comprises an interface betweentwo adjacent layers of a compound substrate. In an array of neighboringcube corner elements, each cube corner element in the array can have atleast one face configured as described above. Further, the cube cornerelements can be made very small (well under 1 mm cube height) due to thedirect machining techniques employed.

[0019] Also disclosed is a method of making a structured surface articlecomprising a geometric structure having a plurality of faces. The methodcomprises the steps of forming an array of geometric structures in afirst surface of a machined substrate; passivating selected locations ofthe first surface of the machined substrate; forming a replicatedsubstrate of the machined substrate to form a compound substrate;forming an array of second geometric structures on a second surfaceopposite the first surface on the machined substrate; and removingselected portions from the second surface of the machined substrate toform an array of neighboring cube corner elements. The cube cornerelements can be PG cube corner elements.

[0020] In another embodiment, the method of making a structured surfacearticle comprises the steps of forming an array of geometric structuresin a first surface of a machined substrate; passivating selectedlocations of the first surface of the machined substrate; forming areplicated substrate of the machined substrate to form a compoundsubstrate; forming an array of second geometric structures on a secondsurface opposite the first surface on the machined substrate; andremoving selected portions from the second surface of the machinedsubstrate to form a geometric structure having a plurality of faces,wherein at least one of the faces is located on the machined substrateand at least one of the faces is located on the replicated substrate.

[0021] In another embodiment, the method of making a geometric structurein an article comprises providing a compound substrate having astructured surface formed along an internal interface between twosubstrates; and forming grooved side surfaces in an exposed surface ofthe compound substrate to form a geometric structure, the geometricstructure comprising a portion of the internal interface and a portionof the grooved side surfaces.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022]FIG. 1 is a plan view of a structured surface comprising one typeof PG cube corner element array, known from the PRIOR ART.

[0023]FIG. 2 is a perspective view of an assembly including a machinedsubstrate.

[0024]FIG. 3 is a sectional view of the substrate of FIG. 2.

[0025]FIG. 4 is a perspective view of the substrate of FIG. 2 after afirst machining operation.

[0026]FIG. 5 is a close-up perspective view of a portion of the machinedsubstrate illustrated in FIG. 4.

[0027]FIG. 6 is a sectional view of an assembly including a compoundsubstrate.

[0028]FIG. 6a is an enlarged section of the compound substrate of FIG.6.

[0029]FIG. 7 is a perspective view of the assembly of FIG. 6 with one ofthe machining bases removed.

[0030]FIG. 8 is a perspective view of the assembly of FIG. 7 with aportion of a blank surrounding the machined substrate removed.

[0031]FIG. 9 is cross-sectional view of the machining of the compoundsubstrate of FIG. 7.

[0032]FIG. 10 is a perspective view of the compound substrate of FIG. 8after the second machining operation.

[0033]FIG. 11 is a top view of FIG. 10. FIGS. 12-14 are top plan viewsof structured surfaces having canted PG cube corner elements, suchsurfaces being capable of fabrication using the methods discussed inconnection with FIGS. 2-11.

[0034]FIG. 15 is a top plan view of an alternate machined substrate inaccordance with the present invention.

[0035]FIG. 16 is a sectional view of the substrate of FIG. 15.

[0036]FIG. 17 is a sectional view of the substrate of FIG. 15 with apassivated surface.

[0037]FIG. 18 is a top plan view of the substrate of FIG. 17 withportions of the passivated surface removed.

[0038]FIG. 19 is a sectional view of the substrate of FIG. 18.

[0039]FIG. 20 is a sectional view of an assembly including a compoundsubstrate.

[0040]FIG. 21 is a top plan view of the machining of the compoundsubstrate of FIG. 20.

[0041]FIG. 22 is a sectional view of the substrate of FIG. 21.

[0042]FIG. 23 is a top plan view of the compound substrate of FIG. 21after the second machining operation.

[0043] In the drawings, the same reference symbol is used forconvenience to indicate elements that are the same or that perform thesame or a similar function.

DETAILED DESCRIPTION OF THE ILLUSTRATIVE EMBODIMENTS

[0044]FIGS. 2 and 3 illustrate an assembly 20 useful for making astructured surface (see FIGS. 9-10) in accordance with the presentinvention. The assembly 20 includes a blank 22 bonded to a firstmachining base 24 by a first bonding layer 26. In the illustratedembodiment, the blank 22 is a continuous structure that includes a deck27 and a series of reference pads 30 a, 30 b, 30 c, 30 d, 30 e, 30 f(collectively referred to as 30) that extend above surface 32. In oneembodiment, the deck 27 has a height 34 generally equal to a height 36of the reference pads 30. The number of reference pads 30 can varydepending upon the application. In an alternate embodiment, the deck 27and the reference pads 30 can be discrete elements bonded to the firstmachining base 24, rather than the continuous blank 22 shown in FIG. 2.

[0045] Blank 22 is composed of a material that can be scribed, cut, orotherwise machined without significant post-machining deformation andwithout substantial burring. This is to ensure that the machined faces,or replications thereof in other substrates, can function as effectiveoptical reflectors. The blank 22 may be constructed from variousmaterials, such as copper, nickel, aluminum, acrylic, or other polymericmaterials. Further discussion on suitable substrate materials is givenbelow. In one embodiment, the blank 22 is a thin metal sheet materialapproximately 0.030 inches thick.

[0046] The blank 22 is bonded to a first machining base 24 using asuitable bonding layer 26, such as epoxy, wax, thermoform or thermosetadhesives, and the like. In the illustrated embodiment, the firstmachining base 24 is a metal plate approximately 2.54 centimeters (1.0inch) thick. The first machining base 24 supports the relatively thinblank 22 and provides reference surfaces 38 for subsequent machiningoperations. Although the circular shape of the assembly 20 is convenientfor subsequent electroplating operations, the circular shape is notrequired.

[0047]FIG. 4 depicts the machining operation to form a machinedsubstrate 28 in the deck portion 27 of the blank 22. Cutting tools 40 a,40 b, 40 c (collectively referred to as 40) move along the deck 27 (seeFIG. 2) to form a structured surface 50 of machined substrate 28,whether by motion of the cutting tools or the substrate or both, to formgroove side surfaces (see FIG. 5). The cutting tool 40 a forms referencegrooves 44 c, 44 f in respective reference pads 30 c, 30 f, cutting tool40 b forms reference grooves 44 a, 44 d in respective reference pads 30a, 30 d, and cutting tool 40 c forms reference grooves 44 b, 44 e inrespective reference pads 30 b, 30 e. A circular reference groove 46 a,46 b, 46 c, 46 d, 46 e, 46 f concentric with the center of the machinedsubstrate 28 is optionally formed in each of the respective referencepads 30. Reference marks 43 may optionally be formed on the edge of themodified blank 22′ to assist in locating the compound substrate 82 toperform the cutting operations illustrated in FIG. 7.

[0048] Each tool 40 is depicted as a so-called “half-angle” tool, whichproduces grooved side surfaces as it progresses through the materialrather than a pair of opposed groove side surfaces, although this is notnecessary. In the illustrated embodiment, one of the grooved sidesurfaces is substantially vertical (see FIG. 5). Consistent with directmachining procedures, cutting tools 40 move along axes 42 a, 42 b, 42 cthat are substantially parallel to the x-y reference plane defined bythe reference surface 38, thus ensuring that the respective groove sidesurfaces also extend along axes that are substantially parallel to thereference plane. In the illustrated embodiment, each of the axes 42 a,42 b, 42 c intersect two of the reference pads 30. Preferably, the axes42 a, 42 b, 42 c are carefully positioned and the tool orientationcarefully selected so that the groove side surfaces have a generallyuniform depth.

[0049] It should be noted that although three cutting tools are shown inFIG. 4, a single cutting tool could be used. The cutting tool can bemade of diamond or other suitably hard material. The machined faces canbe formed by any one of a number of known material removal techniques,for example: milling, where a rotating cutter, spinning about its ownaxis, is tilted and drawn along the surface of the substrate;fly-cutting, where a cutter such as a diamond is mounted on theperiphery of a rapidly rotating wheel or similar structure which is thendrawn along the surface of the substrate; ruling, where a nonrotatingcutter such as a diamond is drawn along the surface of the substrate;and grinding, where a rotating wheel with a cutting tip or edge is drawnalong the surface of the substrate. Of these, preferred methods arethose of fly-cutting and ruling. It is not critical during the machiningoperation whether the cutting tool, the substrate, or both aretranslated relative to the surroundings. Full-angle cutting tools arepreferred when possible over half-angle tools because the former areless prone to breakage and allow higher machining rates. Finally,cutting tools having a curved portion or portions can be used in thedisclosed embodiments to provide non-flat (curved) surfaces or faces inorder to achieve desired optical or mechanical effects.

[0050]FIG. 5 shows an enlarged section of the structured surface 50machined in the machined substrate 28 illustrated in FIG. 4. Structuredsurface 50 includes faces 54 arranged in groups of three that form cubecorner pyramids 56. Interspersed between cube corner pyramids 56 onstructured surface 50 are protrusions 58. The protrusions 58 as showneach have three mutually perpendicular side surfaces 60, three generallyvertical surfaces 61, and a top surface 62. Depending on the procedureused to make the structured surface 50, the generally vertical surfaces61 of the protrusions 58 can be inclined to a greater or lesser extentaway from the vertical. In the illustrated embodiment, the cube cornerpyramids 56 cover about 50% of the machined substrate and theprotrusions 58 cover the other 50% of the substrate.

[0051] The structured surface 50 is then cleaned and passivated. Thepassivation step comprises applying a release layer or modifying thesurface 50 to permit separation of a subsequent replicated substrate 70(see FIG. 6). In an embodiment where the blank 22 is constructed frommetal, such as copper, the structured surface 50 can be passivated withpotassium dichromate or other passive solutions. In an embodiment wherethe blank 22 is constructed from acrylic or another polymeric material,vapor coated or chemically deposited silver can be used to create therelease layer. The passivation step can be modified depending upon thematerial used for the machined substrate 28 and the replicated substrate70.

[0052] In order to permit selective adhesion of the replicated substrate70 to the structured surface 50, the top surfaces 62 of the protrusions58 are treated. In one embodiment, the top surfaces 62 are abraded.Abrasion of the top surfaces 62 can be accomplished using aplanarization process, fly cutting, or a variety of other processes.

[0053]FIGS. 6 and 6a illustrate an assembly 81 that results afterforming a replicated substrate 70 over the machined substrate 28 and thereference pads 30. Electroplating, casting a filler material, and avariety of other techniques can form the replicated substrate 70. Thethickness of the replicated substrate 70 is a matter of design choice.In the illustrated embodiment, the replicated substrate 70 has athickness of about 2 times the height of the desired cube cornerelements.

[0054] As best illustrated in FIG. 6a, due to the previous passivationand abrasion steps, the replicated substrate 70 adheres to thestructured surface 50 along the top surface 62 of the protrusions 58,but not along the passivated surfaces of the pyramids 56 and the sidesurfaces 60, 61 of the protrusions 58. Portions of the replicatedsubstrate 70 protrude into the machined substrate 28 to form a compoundsubstrate 82 (see also FIG. 9). A second machining base 74 is bonded torear surface 76 of the replicated substrate 70 using a suitable bondinglayer 78. Like the first machining base 24, the second machining base 74includes reference surfaces 80 to aid in subsequent machining steps. Thefirst machining base 24 and bonding layer 26 are no longer needed forthe process and are removed from the assembly 20.

[0055]FIG. 7 is a perspective view of an assembly 81 comprising themodified blank 22′ (machined substrate 28 and reference pads 30)selectively bonded to the replicated substrate 70. The replicatedsubstrate 70 is bonded to the second machining base 74 by the bondinglayer 78. In the illustrated embodiment, rear surface 71 of the modifiedblank 22′ is substantially flat. The compound substrate 82 and referencepads 30 embedded in the assembly 81 are shown in phantom for purposes ofillustration only.

[0056] A series of four cuts are made around the perimeter P1, P2, P3,P4 of compound substrate 82, permitting the portions of the modifiedblank 22′ surrounding the machined substrate 28 to be removed from theassembly 81. Reference marks 43 may optionally be used to locate thecompound substrate 82. The passivation layer facilitates removal of thiswaste material. In an embodiment where the blank 22 and replicatedsubstrate 70 are constructed from metal, the portion of the blank 22surrounding the machined substrate 28 is a thin layer that can be peeledfrom the replicated substrate 70.

[0057]FIG. 8 is a perspective view of a modified assembly 83 with theportions of the blank 22 surrounding the compound substrate 82 removed.Surface 85 is of the replicated substrate 70. Surface 90, which extendsabove the surface 85, is the back surface of the machined substrate 28.Reference pad replicas 84 a, 84 b, 84 c, 84 d, 84 e, 84 f (collectivelyreferred to as 84) of the reference pads 30 define cavities in thesurface 85. The reference pad replicas 84 a, 84 d have respectiveparallel ridges 86 a, 86 d, replicas 84 b, 84 e have respective parallelridges 86 b, 86 e, and replicas 84 c, 84 f have respective parallelridges 86 c, 86 f (collectively referred to as 86). Each of thereference pad replicas 84 has a ridge 88 a, 88 b, 88 c, 88 c, 88 d, 88e, 88 f (collectively referred to as 88), respectively, defining acircle concentric with the center of the compound substrate 82. In theillustrated embodiment, the tops of the ridges 86, 88 are generallycoplanar with the surface 85.

[0058]FIG. 9 is a schematic illustration of the machining step performedon the back surface 90 of the machined substrate 28. In the illustratedembodiment, the compound substrate 82 comprises the machined substrate28 and the un-separated replicated substrate 70. The interface 92between the structured surface 50 and the replicated substrate 70 isindicated by dashed line. Bonding at the interface 92, however, islimited to the abraded top surfaces 62 of the protrusions 58. Thepassivation layer prevents or minimizes adhesion along the remainder ofthe interface 92, such as along the pyramids 56 or the side surfaces 60,61 of the protrusions 58.

[0059] The machining step illustrated in FIG. 4 is then performed on theback surface 90 of the machined substrate 28 using the ridges 86, 88 asreference points to guide tool 101. The tool 101 may or may not be ahalf-angle tool. In an embodiment where the machined substrate 28 and/orthe replicated substrate 70 are formed from a transparent orsemi-transparent material, or where the interface between the machinedsubstrate 28 and replicated substrate 70 can be viewed along theperimeter P1, P2, P3, P4 of compound substrate 82, the reference padreplicas 84 may be unnecessary. That is, alignment of the tools 42 a, 42b, 42 c can be accomplished without resort to the reference pad replicas84. Where the machined substrate 28 is formed from an opaque materialsuch as metal, the reference pad replicas 84 (and particularly theridges 86) provide precise reference points so that the machining stepillustrated in FIG. 9 can be performed.

[0060] After cuts are made along all three axes 42 a, 42 b, 42 c, wasteportions 94 of the machined substrate 28 fall away or are removed,leaving a cube corner cavity 118 in the replicated substrate 70. In someembodiments, the tool 101 may cut into the replicated substrate 70 suchthat the replicated substrate may include a replicated or formed portionand a machined portion. The distal ends or top surfaces 62 of thediscrete pieces or protrusions 58 from the machined substrate 28 arebonded to the replicated substrate 70. Bottom or proximal portions ofthe protrusions 58 are machined to form cube corner pyramids 120 a. Theprotrusions 58 on the machined substrate 28 remain embedded in thereplicated substrate 70. Once all of the waste portions 94 of themachined substrate 28 are removed from the replicated substrate 70, thecube corner pyramids 120 a and cube corner cavities 118 form a geometricstructured surface 100 with an array of PG cube corner elements (seeFIG. 10).

[0061]FIG. 10 is a view of a geometric structured surface 100 oncompound substrate 82 after all groove side surfaces have been formed.Each of the cube corner cavities 118 has three replicated faces 116 a,116 b, 116 c and each of the cube corner pyramids 120 a has threemachined faces 126 a, 126 b, 126 c, configured approximately mutuallyperpendicular to each other. In the case where the three faces of a cubecorner pyramid 120 a are substantially aligned with adjacent faces 116of cavities 118, and where such cavities 118 have a common orientation,the three faces of cube corner pyramid 120 a (when consideredseparately) form a “truncated” cube corner pyramid. Such a pyramid ischaracterized by having exactly three nondihedral edges that form a“base triangle” in the plane of the structured surface.

[0062] Each of the three faces 126 a-c of the cube corner pyramids 120 aare machined to be substantially aligned with the nearest face 116 of anadjacent cube corner cavity 118. Consequently, each new cube cornercavity 132 comprising one replicated cube corner cavity 118 and onemachined face 126 from each of its neighboring geometric structures 120a. Reference numeral 132 a shows in bold outline one such cube cornercavity 132. A given face of one of the cube corner cavities 132comprises one face of a cube corner cavity 118 formed in the replicatedsubstrate 70 and one of the faces 126 a, 126 b, or 126 c machined in themachined substrate 28. As will be discussed infra, faces 116 of the cubecorner cavity 118 are machined in the replicated substrate 70.Therefore, each cube corner cavity 132 comprises a compound face made upof a portion substantially formed or replicated in the replicatedsubstrate 70 and a portion machined in the machined substrate 28separated by a transition line 130. The transition lines 130 lie alongthe boundary or interface between the machined substrate 28 and thereplicated substrate 70.

[0063] One can also identify new cube corner pyramids 134 formed on thestructured surface shown in FIG. 10. Each cube corner pyramid 134comprises one geometric structure 120 a, which is a cube corner pyramid,and one face each of its neighboring cube corner cavities 118. Each faceof one of the pyramids 134 is a compound face comprising a face 116 ofone of the cavities 118 in the replicated substrate 70 and a machinedface from structure 120 a formed from the machined substrate 28.Reference numeral 134 a shows in bold outline of one such cube cornerpyramid 134. Note that the reference points 122 locate the uppermostextremities or peaks of the pyramids 134. Both cube corner pyramids 134and cube corner cavities 132 are PG cube corner elements, since bothhave a face terminating at a nondihedral edge of the cube cornerelement, such nondihedral edge being nonparallel to reference plane x-y.

[0064]FIG. 11 shows a top view of the structured surface of FIG. 10.Transition lines 130 are drawn narrower than other lines to aid inidentifying the PG cube corner elements, i.e. cube corner cavities 132and cube corner pyramids 134. The compound faces of such PG cube cornerelements extend across opposite sides of the transition lines 130separating discrete pieces of the machined substrate 28 from thereplicated substrate 70, to which they are bonded. In the illustratedembodiment, all transition lines 130 lie in a common plane referred toas a transition plane, which in the case of this embodiment is coplanarwith the x-y plane. The faces of the structured surface machined in themachined substrate 28 are disposed on one side of the transition planeand the faces machined in the replicated substrate 70 are disposed onthe other side.

[0065] The machined cube corner article of FIGS. 10-11 can itselffunction as a retroreflective article, both with respect to lightincident from above (by virtue of cube corner cavities 132) and, wherethe substrate is at least partially transparent, with respect to lightincident from below (by virtue of cube corner pyramids 134). In eithercase, depending upon the composition of the substrate, a specularlyreflective thin coating such as aluminum, silver, or gold can be appliedto the structured surface to enhance the reflectivity of the compoundfaces. In the case where light is incident from below, reflectivecoatings can be avoided in favor of an air interface that provides totalinternal reflection.

[0066] More commonly, however, the compound substrate of FIGS. 10-11 isused as a mold from which end-use retroreflective articles are made,whether directly or through multiple generations of molds, usingconventional replication techniques. Each mold or other article madefrom the compound substrate will typically contain cube corner elementshaving at least one face terminating at a nondihedral edge of the cubecorner element, the at least one face comprising two constituent facesdisposed on opposed sides of a transition line, the transition linebeing nonparallel to such nondihedral edge. As seen from FIGS. 10-11,transition lines 130 lie in the transition plane coincident with the x-yplane, whereas nondihedral edges shown in bold for both PG cube cornercavity 132 and PG cube corner pyramid 134 are inclined relative to thex-y plane. It is also possible to fabricate surfaces where thetransition lines do not all lie in the same plane, by forming grooveside surfaces at different depths in the substrate.

[0067] Transition lines can in general take on a great variety of forms,depending upon details of the cutting tool used and on the degree towhich the motion of the cutting tool is precisely aligned with otherfaces in the process of forming groove side surfaces. Although in manyapplications transition lines are an artifact to be minimized, in otherapplications they can be used to advantage to achieve a desired opticalresult such as a partially transparent article. A detailed discussion ofvarious transition line configurations is set forth in commonly assignedU.S. patent application Ser. No. ______ (Attorney Docket No. 54222USA_A)filed on the same date herewith, entitled Structured Surface ArticlesContaining Geometric Structures with Compound Faces and Methods forMaking Same, which is incorporated by reference.

[0068] A wide variety of structured surfaces can be fabricated using thepresent compound substrate 82 and the machining technique describedabove. The PG cube corner elements of FIG. 11 each have a symmetry axisthat is perpendicular to the x-y reference plane of the structuredsurface. Cube corner elements typically exhibit the highest opticalefficiency in response to light incident on the element roughly alongthe symmetry axis. The amount of light retroreflected by a cube cornerelement generally drops as the incidence angle deviates from thesymmetry axis. FIG. 12 shows a top plan view of a structured surface 136similar to that of FIG. 11, extending along the x-y plane, except thatthe PG cube corner elements of FIG. 12 are all canted such that theirsymmetry axes are tilted with respect to the normal of the structuredsurface. The symmetry axis for each PG cube corner cavity 146 in FIG. 12lies in a plane parallel to the y-z plane, having a vertical componentin the +z direction (out of the page) and a transverse component in the+y direction. Symmetry axes for the PG cube corner pyramids 148 of FIG.12 point in the opposite direction, with components in the −z and −ydirections. In fabricating surface 136, a compound substrate is usedwherein the protrusions of generally triangular cross-section areisosceles in shape, rather than equilateral as in FIG. 1.

[0069] Four distinct types of cube corner elements are present on thestructured surface 136: truncated cube corner cavities formed inreplicated substrate 70 and a triangular outline in plan view; truncatedcube corner pyramids having faces machined in discrete pieces of themachined substrate 28 and triangular outline; PG cube corner cavitieshaving compound faces and a hexagonal outline; and PG cube cornerpyramids, also having compound faces and a hexagonal outline. Arepresentative cube corner cavity formed in the replicated substrate 70is identified in FIG. 12 by bold outline 140, and a representative cubecorner pyramid machined in the machined substrate 28 is identified bybold outline 142. Transition lines 144 separate machined from formed orreplicated faces, and all such lines 144 lie in a transition planeparallel to the x-y plane. In other embodiments, the transition linesmay lie parallel to a transition plane but not be coplanar. Selectedfaces of cavities 140 and pyramids 142 form canted PG cube cornerelements, in particular canted PG cube corner cavities 146 and canted PGcube corner pyramids 148. Reference points 122, as before, identifylocalized tips or peaks disposed above the x-y plane.

[0070]FIG. 13 shows a structured surface 136 a similar to that of FIG.12, and like features bear the same reference numeral as in FIG. 12 withthe added suffix “a”. PG cube corner elements of FIG. 13 are canted withrespect to the normal of structured surface 136 a, but in a differentdirection compared to that of the PG cube corner elements of FIG. 12.The symmetry axis for each PG cube corner cavity 146 a is disposed in aplane parallel to the y-z plane, and has a vertical component in the +zdirection and a transverse component in the −y direction.

[0071]FIG. 14 shows a structured surface similar to that of FIGS. 12 and13, and like features bear the same reference numeral as in FIG. 12 withthe added suffix “b”. PG cube corner elements in FIG. 14 are alsocanted, but, unlike the PG cube corner elements of FIGS. 12 and 13, thedegree of cant is such that the outline in plan view of each PG cubecorner element has no mirror-image plane of symmetry. The cube cornercavities of FIG. 14 each have a symmetry axis that has components in the+z, +y, and −x direction. It will be noted that the triangles formed bytransition lines 144 (FIG. 12) are isosceles triangles each having onlyone included angle less than 60 degrees; triangles formed by lines 144 a(FIG. 13) are isosceles triangles each having only one included anglegreater than 60 degrees; and triangles formed by lines 144 b (FIG. 14)are scalene triangles. Representative values in degrees for the includedangles of triangles defined by transition lines 144 a are, respectively:(70, 70, 40); (80, 50, 50); and (70, 60, 50).

[0072] The embodiments discussed above have associated therewith anasymmetrical entrance angularity (i.e., when rotated about an axiswithin the plane of the sheeting). Embodiments with symmetrical entranceangularity are also possible, such as the matched-pair cube cornerstructure discussed in connection with FIGS. 15-23.

[0073]FIGS. 15 and 16 depict an alternate machined substrate 200 inaccordance with the present invention. The machined substrate 200 isbonded to a first machining base 202 by a first bonding layer 204. Twosets of grooves 206, 208 parallel to axis 207 a 207 b, respectively, areformed using tools 201 a, 201 b to define a machined surface 212. In theillustrated embodiment, the machined surface 212 includes faces 213arranged in groups of four that form four-sided pyramids 210 having anapex or reference point 215. The four-sided pyramids 210 are arranged inrows 217, 222, 223. Other geometric structures 211 are also formed bythe grooves 206, 208.

[0074] As illustrated in sectional view FIG. 17, the machined surface212 is then cleaned and passivated. The passivation step comprisesapplying a release layer or making a surface modification 216 (referredto collectively as “passivated surface”) on the machined surface 212 topermit separation of a subsequent replicated substrate 214 (see FIG.20). In one embodiment, the passivated surface is formed on only aportion of the machined surface 212.

[0075] As illustrated in FIGS. 18 and 19, additional grooves 220 a, 220b, 220 c (referred to collectively as 220) are formed in the machinedsurface 212 parallel to axis 207 c using tool 201 c in order to removeportions of some of the geometric structures 211. The grooves 220 alsoremove some of the surface modification 216 to permit selective adhesionof the replicated substrate 214 (see FIG. 20) to the machined surface212. As best illustrated in FIG. 19, the passivated surface 216 is notpresent along flat regions 228 or along side walls 230, while thepassivated surface 216 on faces 213 is substantially intact.

[0076]FIG. 20 illustrates an assembly 232 that results after forming areplicated substrate 214 over the machined substrate 200′.Electro-plating, casting a filler material, and a variety of othertechniques can form the replicated substrate 214. Due to the previouspassivation step, the replicated substrate 214 adheres to the flatregions 228 and side walls 230, but not along the passivated surfaces216. Portions 234 of the replicated substrate 214 protrude into, andbond with, the machined substrate 200′ along surfaces 228, 230 to form acompound substrate 236. A second machining base 250 is bonded to rearsurface 252 of the replicated substrate 214 using a suitable bondinglayer 254. Like the first machining base 202, the second machining base250 includes reference surfaces (see FIG. 3) to aid in subsequentmachining steps. The first machining base 202 and bonding layer 204 areno longer needed for the process and are removed from the assembly 232.The second machining base 250 supports the compound substrate 236 duringmachining of the back surface 260, discussed below.

[0077]FIGS. 21 and 22 illustrate the machining step performed on theback surface 260 of the compound substrate 236. Grooves 268 a, 268 b,268 c are formed along axes 270 a, 270 b, 270 c using tools 272 a, 272b, 272 c. The grooves 268 a, 268 b, 268 c may extend into the replicatedsubstrate 214. Waste portions 274 are not bonded to the replicatedsubstrate 214 because of the passivation layer 216. Consequently, afterthe grooves 268 are made along all three axes 270, waste portions 274fall away or are removed, leaving four-sided cavities 276 in thereplicated substrate 214.

[0078] Discrete pieces or portions 278, 280 of the compound substrate236, however, are bonded to the replicated substrate 214 along surfaces230. Bottom or proximal portions of the portions 278, 280 are machinedto form three-sided pyramids 282. The portions 278, 280 of the machinedsubstrate 200′ remain embedded in the replicated substrate 214 portionof the compound substrate 236. Once all of the waste portions 274 of thecompound substrate 236 are removed from the replicated substrate 214,thus exposing all of the four-sided cavities 276, the three-sidedpyramids 282 and four-sided cavities 276 form a geometric structuredsurface 290 comprising an array of PG cube corner elements (see FIG.23).

[0079] In an embodiment where the machined substrate 200′ and/or thereplicated substrate 214 are formed from a transparent orsemi-transparent material, or where the interface between the machinedsubstrate 200′ and replicated substrate 214 can be viewed along theperimeter of compound substrate 236, reference pads such as illustratedin connection with FIGS. 2-8 may be unnecessary. That is, alignment ofthe tools can be accomplished without resort to the reference pad. Wherethe machined substrate 200′ is formed from an opaque material such asmetal, reference pads such as illustrated in FIG. 2 provide precisereference points so that the machining step illustrated in FIG. 21 canbe performed.

[0080]FIG. 23 illustrates the geometric structured surface 290 after allgroove side surfaces have been formed. This geometry results in twodifferent types of PG cube corner elements on the structured surface.Cube corner pyramid 296 has face g and compound faces h, h′; i, i′separated by transition lines a and b, respectively. Cube corner pyramid298 has face j and compound faces k, k′; 1,1′ separated by transitionlines c and d, respectively. Faces g and j are polygons with more thanthree sides. Consequently, in the top view of FIG. 23, the cube cornerpyramids 296, 298 each have a rectangular shape as shown by therespective dashed outlines, rather than a hexagonal outline as depictedin FIGS. 10-14. In an embodiment where the grooves 272 c are all of thesame depth, the cube corner elements 296 and 298 are opposing or matchedpair cube corner elements that provide symmetric entrance angularity.Depending upon the aspect ratio, the plan view rectangular outlines ofthe cube corner elements can also include a square outline.

[0081] Cube corner elements of FIG. 23 can be (forward or backward)canted or uncanted as desired. Producing cube corner elements that arecanted to a greater or lesser degree is accomplished by tailoring theshape of the diamond-shaped protrusions and then the orientation of thegroove side surfaces (g, h, i, j, k, l) to be in conformance with thedesired degree of canting. If canting is used, then such matched pairscan, in keeping with principles discussed in U.S. Pat. Nos. 4,588,258(Hoopman), 5,812,315 (Smith et al.), and 5,822,121 (Smith et al.), giverise to widened retroreflective angularity so that an article having thestructured surface will be visible over a widened range of entranceangles.

[0082] During the present machining process, the cutting tool removes arelatively large amount of material because the angle between thesteeply inclined side wall and the subsequent machined face is often inexcess of 10 degrees, typically ranging from about 10 to about 45degrees. Some of the groove side surfaces can then be formed in such amodified machined substrate by leaving more material on the cavities orprotrusions during either or both machining steps, thereby reducing toolforces which could detrimentally cause distortions. Another benefit isless wear on the cutting tool. A modified machined substrate can also beused as a master from which future generations of positive/negativemolds can be made. Various geometric configurations for modifiedmachined substrate are disclosed in commonly assigned U.S. patentapplication Ser. No. ______ (Attorney Docket No. 54222USA1A) filed onthe same date herewith, entitled Structured Surface Articles ContainingGeometric Structures with Compound Faces and Methods for Making Same,which is incorporated by reference.

[0083] The cube corner elements disclosed herein can be individuallytailored so as to distribute light retroreflected by the articles into adesired pattern or divergence profile, as taught by U.S. Pat. No.4,775,219 (Appledorn et al.). For example, compound faces that make upthe PG cube corner elements can be arranged in a repeating pattern oforientations that differ by small amounts, such as a few arc-minutes,from the orientation that would produce mutual orthogonality with theother faces of cube corner element. This can be accomplished bymachining groove side surfaces (both those that ultimately become thefaces in the finished mold below the transition plane as well as thosethat become faces in the finished mold above the transition plane) atangles that differ from those that would produce mutually orthogonalfaces by an amount known as a “groove half-angle error”. Typically thegroove half-angle error introduced will be less than ±20 arc minutes andoften less than ±5 arc minutes. A series of consecutive parallel grooveside surfaces can have a repeating pattern of groove half-angle errorssuch as abbaabba . . . or abcdabcd . . . , where a, b, c, and d areunique positive or negative values. In one embodiment, the pattern ofgroove half-angle errors used to form faces in the finished mold abovethe transition plane can be matched up with the groove half-angle errorsused to form faces in the finished mold below the transition plane. Inthis case, the portions of each compound face on the machined substrateand the replicated substrate will be substantially angularly alignedwith each other. In another embodiment, the pattern used to form one setof faces can differ from the pattern used to form the other, as wherethe faces below the transition plane incorporate a given pattern ofnonzero angle errors and faces above the transition plane incorporatesubstantially no angle errors or a different pattern of non-zero errors.In this latter case, the portions of each compound face on the machinedsubstrate and the replicated substrate will not be precisely angularlyaligned with each other.

[0084] Advantageously, such substrates can serve as a master substratefrom which future generations of positive/negative molds can be made,all having the same general shape of cube corner element in plan viewbut having slightly different face configurations. One such daughtermold can incorporate cube corner elements that each have compound faceswhose constituent faces are aligned, the compound faces all beingmutually perpendicular to the remaining faces of the cube cornerelement. Another such daughter mold can incorporate cube corner elementsthat also have compound faces whose constituent faces are aligned, butthe compound faces can differ from orthogonality with remaining faces ofthe cube corner element. Still another such daughter mold canincorporate cube corner elements that have compound faces whoseconstituent faces are not aligned. All such daughter molds can be madefrom a single master mold with a minimal amount of material removed bymachining.

[0085] The working surface of the mold substrates can have any suitablephysical dimensions, with selection criteria including the desired sizeof the final mold surface and the angular and translational precision ofthe machinery used to cut the groove surfaces. The working surface has aminimum transverse dimension that is greater than two cube cornerelements, with each cube corner element having a transverse dimensionand/or cube height preferably in the range of about 25 μm to about 1 mm,and more preferably in the range of about 25 μm to about 0.25 mm. Theworking surface is typically a square several inches on a side, withfour inch (10 cm) sides being standard. Smaller dimensions can be usedto more easily cut grooves in registration with formed surfaces over thewhole structured surface. The substrate thickness can range from about0.5 to about 2.5 mm. (The measurements herein are provided forillustrative purposes only and are not intended to be limiting.) A thinsubstrate can be mounted on a thicker base to provide rigidity. Multiplefinished molds can be combined with each other e.g. by welding in knowntiling arrangements to yield a large tiled mold that can then be used toproduce tiled retroreflective products.

[0086] In the manufacture of retroreflective articles such asretroreflective sheeting, the structured surface of the machinedsubstrate is used as a master mold that can be replicated usingelectroforming techniques or other conventional replicating technology.The structured surface can include substantially identical cube cornerelements or can include cube corner elements of varying sizes, geometry,or orientations. The structured surface of the replica, sometimesreferred to in the art as a ‘stamper’, contains a negative image of thecube corner elements. This replica can be used as a mold for forming aretroreflective article. More commonly, however, a large number ofsuitable replicas are assembled side-by-side to form a tiled mold largeenough to be useful in forming tiled retroreflective sheeting.Retroreflective sheeting can then be manufactured as an integralmaterial, e.g. by embossing a preformed sheet with an array of cubecorner elements as described above or by casting a fluid material into amold. See, JP 8-309851 and U.S. Pat. No. 4,601,861 (Pricone).Alternatively, the retroreflective sheeting can be manufactured as alayered product by casting the cube corner elements against a preformedfilm as taught in PCT application No. WO 95/11464 (Benson, Jr. et al.)and U.S. Pat. No. 3,684,348 (Rowland) or by laminating a preformed filmto preformed cube corner elements. By way of example, such sheeting canbe made using a nickel mold formed by electrolytic deposition of nickelonto a master mold. The electroformed mold can be used as a stamper toemboss the pattern of the mold onto a polycarbonate film approximately500 μm thick having an index of refraction of about 1.59. The mold canbe used in a press with the pressing performed at a temperature ofapproximately 175° to about 200° C.

[0087] The various mold substrates discussed above can generally becategorized into two groups: replicated substrates, which receive atleast part of their structured surface by replication from a priorsubstrate, and bulk substrates, which do not. Suitable materials for usewith bulk mold substrates are well known to those of ordinary skill inthe art, and generally include any material that can be machined cleanlywithout burr formation and that maintains dimensional accuracy aftergroove formation. A variety of materials such as machinable plastics ormetals may be utilized. Acrylic is an example of a plastic material;aluminum, brass, electroless nickel, and copper are examples of useablemetals.

[0088] Suitable materials for use with replicated mold substrates thatare not subsequently machined are well known to those of ordinary skillin the art, and include a variety of materials such as plastics ormetals that maintain faithful fidelity to the prior structured surface.Thermally embossed or cast plastics such as acrylic or polycarbonate canbe used. Metals such as electrolytic nickel or nickel alloys are alsosuitable.

[0089] Suitable materials for use with replicated mold substrates whosestructured surface is subsequently machined are also well known to thoseof ordinary skill in the art. Such materials should have physicalproperties such as low shrinkage or expansion, low stress, and so onthat both ensure faithful fidelity to the prior structured surface andthat lend such materials to diamond machining. A plastic such as acrylic(PMMA) or polycarbonate can be replicated by thermal embossing and thensubsequently diamond machined. Suitable hard or soft metals includeelectrodeposited copper, electroless nickel, aluminum, or compositesthereof.

[0090] With respect to retroreflective sheeting made directly orindirectly from such molds, useful sheeting materials are preferablymaterials that are dimensionally stable, durable, weatherable andreadily formable into the desired configuration. Examples of suitablematerials include acrylics, which generally have an index of refractionof about 1.5, such as Plexiglas resin from Rohm and Haas; thermosetacrylates and epoxy acrylates, preferably radiation cured,polycarbonates, which have an index of refraction of about 1.6;polyethylene-based ionomers (marketed under the name ‘SURLYN’);polyesters; and cellulose acetate butyrates. Generally any opticallytransmissive material that is formable, typically under heat andpressure, can be used. Other suitable materials for formingretroreflective sheeting are disclosed in U.S. Pat. No. 5,450,235 (Smithet al.). The sheeting can also include colorants, dyes, UV absorbers, orother additives as needed.

[0091] It is desirable in some circumstances to provide retroreflectivesheeting with a backing layer. A backing layer is particularly usefulfor retroreflective sheeting that reflects light according to theprinciples of total internal reflection. A suitable backing layer can bemade of any transparent or opaque material, including colored materials,that can be effectively engaged with the disclosed retroreflectivesheeting. Suitable backing materials include aluminum sheeting,galvanized steel, polymeric materials such as polymethyl methacrylates,polyesters, polyamids, polyvinyl fluorides, polycarbonates, polyvinylchlorides, polyurethanes, and a wide variety of laminates made fromthese and other materials.

[0092] The backing layer or sheet can be sealed in a grid pattern or anyother configuration suitable to the reflecting elements. Sealing can beaffected by use of a number of methods including ultrasonic welding,adhesives, or by heat sealing at discrete locations on the arrays ofreflecting elements (see, e.g. U.S. Pat. No. 3,924,928). Sealing isdesirable to inhibit the entry of contaminants such as soil and/ormoisture and to preserve air spaces adjacent the reflecting surfaces ofthe cube corner elements.

[0093] If added strength or toughness is required in the composite,backing sheets of polycarbonate, polybutryate or fiber-reinforcedplastic can be used. Depending upon the degree of flexibility of theresulting retroreflective material, the material can be rolled or cutinto strips or other suitable designs. The retroreflective material canalso be backed with an adhesive and a release sheet to render it usefulfor application to any substrate without the added step of applying anadhesive or using other fastening means.

Glossary of Selected Terms

[0094] An “array of neighboring cube corner elements” means a given cubecorner element together with all adjacent cube corner elements borderingit.

[0095] “Compound face” means a face composed of at least twodistinguishable faces (referred to as “constituent faces”) that areproximate each other. The constituent faces are substantially alignedwith one another, but they can be offset translationally and/orrotationally with respect to each other by relatively small amounts(less than about 10 degrees of arc, and preferably less than about 1degree of arc) to achieve desired optical effects as described herein.

[0096] “Compound substrate” means a substrate formed from a machinedsubstrate having a structured surface and a replicated substrate(collectively referred to as “layers”) bonded along at least a portionof the interface with the machined substrate. One or more of the layersof the compound substrate may be discontinuous.

[0097] “Cube corner cavity” means a cavity bounded at least in part bythree faces arranged as a cube corner element.

[0098] “Cube corner element” means a set of three faces that cooperateto retroreflect light or to otherwise direct light to a desiredlocation. Some or all of the three faces can be compound faces. “Cubecorner element” also includes a set of three faces that itself does notretroreflect light or otherwise direct light to a desired location, butthat if copied (in either a positive or negative sense) in a suitablesubstrate forms a set of three faces that does retroreflect light orotherwise direct light to a desired location.

[0099] “Cube corner pyramid” means a mass of material having at leastthree side faces arranged as a cube corner element.

[0100] “Cube height” means, with respect to a cube corner element formedon or formable on a substrate, the maximum separation along an axisperpendicular to the substrate between portions of the cube cornerelement.

[0101] “Dihedral edge” of a cube corner element is an edge of one of thethree faces of the cube corner element that adjoins one of the two otherfaces of the same cube corner element. Note that any particular edge ona structured surface may or may not be a dihedral edge, depending uponwhich cube corner element is being considered.

[0102] “Direct machining” refers to forming in the plane of a substrateone or more groove side surfaces typically by drawing a cutting toolalong an axis substantially parallel to the plane of the substrate.

[0103] “Face” means a substantially smooth surface.

[0104] “Geometric structure” means a protrusion or cavity having aplurality of faces.

[0105] “Groove” means a cavity elongated along a groove axis and boundedat least in part by two opposed groove side surfaces.

[0106] “Groove side surface” means a surface or series of surfacescapable of being formed by drawing one or more cutting tools across asubstrate in a substantially continuous linear motion. Such motionincludes fly-cutting techniques where the cutting tool has a rotarymotion as it advances along a substantially linear path.

[0107] “Nondihedral edge” of a cube corner element is an edge of one ofthe three faces of the cube corner element that is not a dihedral edgeof such cube corner element. Note that any particular edge on astructured surface may or may not be a nondihedral edge, depending uponwhich cube corner element is being considered.

[0108] “PG cube corner element” stands for “preferred geometry” cubecorner element, and is defined in the context of a structured surface ofcube corner elements that extends along a reference plane. For thepurposes of this application, a PG cube corner element means a cubecorner element that has at least one nondihedral edge that: (1) isnonparallel to the reference plane; and (2) is substantially parallel toan adjacent nondihedral edge of a neighboring cube corner element. Acube corner element whose three reflective faces are all rectangles(inclusive of squares) is one example of a PG cube corner element.

[0109] “Protrusion” has its broad ordinary meaning, and can comprise apyramid.

[0110] “Pyramid” means a protrusion having three or more side faces thatmeet at a vertex, and can include a frustum.

[0111] “Reference plane” means a plane or other surface thatapproximates a plane in the vicinity of a group of adjacent cube cornerelements or other geometric structures, the cube corner elements orgeometric structures being disposed along the plane.

[0112] “Retroreflective” means having the characteristic that obliquelyincident incoming light is reflected in a direction antiparallel to theincident direction, or nearly so, such that an observer at or near thesource of light can detect the reflected light.

[0113] “Structured” when used in connection with a surface means asurface that has a plurality of distinct faces arranged at variousorientations.

[0114] “Symmetry axis” when used in connection with a cube cornerelement refers to the vector that originates at the cube corner apex andforms an equal acute angle with the three faces of the cube cornerelement. It is also sometimes referred to as the optical axis of thecube corner element.

[0115] “Transition line” means a line or other elongated feature thatseparates constituent faces of a compound face.

[0116] “Waste pieces” means portions of the compound substrate that arediscarded using the present fabrication methods.

[0117] All patents and patent applications referred to herein areincorporated by reference. Although the present invention has beendescribed with reference to preferred embodiments, workers skilled inthe art will recognize that changes can be made in form and detailwithout departing from the spirit and scope of the invention.

What is claimed is:
 1. A geometric structure having a plurality of facesdisposed on a compound substrate, the compound substrate comprising amachined substrate and a substantially replicated substrate, wherein atleast one of the faces is located on the machined substrate and at leastone of the faces is located on the replicated substrate.
 2. Thegeometric structure of claim 1, wherein the geometric structurecomprises a cube corner element.
 3. The geometric structure of claim 1,wherein at least one of the faces comprises a compound face, wherein aportion of the compound face is located on the machined substrate and aportion of the compound face is located on the replicated substrate. 4.The geometric structure of claim 3, wherein the portion of the compoundface on the machined substrate is substantially aligned with the portionon the replicated substrate.
 5. The geometric structure of claim 3,wherein the portion of the compound face on the machined substrate andthe portion on the replicated substrate have angular orientations thatdiffer by less than 10 degrees of arc.
 6. The geometric structure ofclaim 3, wherein the compound face has a transition line separating theportion on the machined substrate from the portion on the replicatedsubstrate.
 7. The geometric structure of claim 6, wherein the compoundface terminates at a nondihedral edge of a cube corner element, andwherein the transition line is nonparallel to the nondihedral edge. 8.The geometric structure of claim 1, wherein the geometric structurecomprises a cube corner element having an outline in plan view selectedfrom the group of shapes consisting of a hexagon and a rectangle.
 9. Amold comprising a plurality of geometric structures set forth inclaim
 1. 10. The mold of claim 9, wherein the plurality of geometricstructures comprise a plurality of cube corner elements.
 11. The mold ofclaim 10, wherein at least some of the plurality of cube corner elementsare PG cube corner elements.
 12. The mold of claim 10, wherein theplurality of cube corner elements are part of a structured surface thatcomprises cavities formed in the replicated substrate and pyramidsformed at least in part on the machined substrate.
 13. The mold of claim10, wherein at least some of the cube corner elements are arranged inopposing orientations.
 14. The mold of claim 10, wherein at least someof the cube corner elements are canted and form matched pairs of cubecorner elements.
 15. A retroreflective article made by at least onereplication from the mold of claim
 11. 16. A compound substratecomprising a substantially replicated substrate having a structuredsurface and a discontinuous machined substrate covering only a portionof the structured surface, the compound substrate also comprising atleast one geometric structure having at least one face disposed on thestructured surface and at least another face disposed on the machinedsubstrate.
 17. The substrate of claim 16 wherein the geometric structurecomprises a cube corner element having a cube height of no greater thanabout 1 mm, the at least one face and the at least another face beingdisposed on opposite sides of a transition line that is nonparallel to adihedral edge of the cube corner element.
 18. The substrate of claim 16,wherein the at least one face and the at least another face are disposedon opposite sides of a transition line, wherein substantially alltransition lines are parallel to a reference plane.
 19. The substrate ofclaim 16, wherein the geometric structure comprises a cube cornerelement having an outline in plan view selected from the group of shapesconsisting of a hexagon and a rectangle.
 20. A compound substratecomprising a substantially replicated substrate and a machinedsubstrate, the replicated substrate having a structured surface and themachined substrate disposed in discrete pieces on the structuredsurface.
 21. The compound substrate of claim 20, wherein the structuredsurface comprises cavities and the discrete pieces comprise a pluralityof pyramids that are adjacent to the cavities.
 22. The compoundsubstrate of claim 21, wherein the pyramids and cavities form cubecorner elements that have associated therewith a symmetrical entranceangularity.
 23. A cube corner article made by at least one replicationfrom the substrate of claim
 20. 24. A method of making a geometricstructure in an article, comprising the steps of: providing a compoundsubstrate having a structured surface formed along an internal interfacebetween two substrates; and forming grooved side surfaces in an exposedsurface of the compound substrate to form a geometric structure, thegeometric structure comprising a portion of the internal interface and aportion of the grooved side surfaces.
 25. The method of claim 24,wherein the geometric structure comprises one of a cube corner elementor a PG cube corner element.
 26. The method of claim 24, wherein theproviding step comprises the steps of: passivating a surface of at leastone of the two substrates; and selectively removing portions of thepassivated surface.
 27. The method of claim 24, wherein the forming stepcomprises forming an array of cube corner elements, which array includesthe geometric structure.
 28. The method of claim 27, wherein at leastsome of the cube corner elements are canted and arranged in opposingorientations.
 29. The method of claim 24, further comprising forming atleast one reference mark in at least one of the two substrates.
 30. Themethod of claim 24, wherein the grooved side surfaces extend along axesthat are parallel to a common plane.
 31. The method of claim 24, whereinthe providing step comprises: providing a first substrate; forming aplurality of faces in a first surface of the first substrate; andforming a second substrate over the plurality of faces as a replica. 32.The method of claim 31, wherein the forming a plurality of faces in thefirst surface comprises forming at least two intersecting sets ofparallel v-shaped grooves.
 33. The method of claim 24, wherein the stepof forming grooved side surfaces produces discrete pieces of one of thetwo substrates on the other substrate, the method further comprising thestep of: removing at least some of the discrete pieces to exposeportions of the internal interface.
 34. The method of claim 24, furthercomprising the step of: replicating the geometric structure to formretroreflective sheeting.
 35. The method of claim 24, wherein the stepof forming grooved side surfaces comprises the step of forming aplurality of geometric structures selected from the group consisting ofthree-sided geometric structures and four-sided geometric structures.36. A method of making a structured surface article comprising ageometric structure having a plurality of faces, the method comprisingthe steps of: forming a plurality of faces in a first surface of amachined substrate; forming a replicated substrate of the machinedsubstrate to form a compound substrate; forming a plurality of faces ina second surface of the machined substrate opposite the first surface;and removing selected portions of the machined substrate to form ageometric structure having at least a first face disposed on themachined substrate and at least a second face disposed on the replicatedsubstrate.
 37. The method of claim 36, wherein the geometric structureis one of a plurality of geometric structures each comprising a cubecorner element, at least some of the cube corner elements being arrangedin opposing orientations.